Information on Result #657756
Linear OA(25616, 257, F256, 16) (dual of [257, 241, 17]-code or 257-arc in PG(15,256)), using algebraic-geometric code AG(F,120P) with degPÂ =Â 2 based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
- Extended Reed–Solomon Code [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1632, 514, F16, 16) (dual of [514, 482, 17]-code) | [i] | Trace Code | |
| 2 | Linear OA(1631, 257, F16, 16) (dual of [257, 226, 17]-code) | [i] | Base Reduction for Projective Spaces | |
| 3 | OA(3226, 257, S32, 16) | [i] | Discarding Parts of the Base for OAs | |
| 4 | OA(6422, 257, S64, 16) | [i] | ||
| 5 | OA(12819, 257, S128, 16) | [i] | ||
| 6 | Linear OA(25649, 514, F256, 33) (dual of [514, 465, 34]-code) | [i] | (u, u+v)-Construction | |
| 7 | Linear OA(25650, 517, F256, 33) (dual of [517, 467, 34]-code) | [i] | ||
| 8 | Linear OA(25648, 514, F256, 32) (dual of [514, 466, 33]-code) | [i] | ||
| 9 | Linear OA(25649, 517, F256, 32) (dual of [517, 468, 33]-code) | [i] | ||
| 10 | Linear OA(25624, 514, F256, 16) (dual of [514, 490, 17]-code) | [i] | ||
| 11 | Linear OA(25650, 546, F256, 33) (dual of [546, 496, 34]-code) | [i] | ||
| 12 | Linear OA(25649, 546, F256, 32) (dual of [546, 497, 33]-code) | [i] | ||
| 13 | Linear OA(25619, 260, F256, 18) (dual of [260, 241, 19]-code) | [i] | ✔ | Construction X with Algebraic-Geometric Codes |
| 14 | Linear OA(25617, 260, F256, 16) (dual of [260, 243, 17]-code) | [i] | ✔ | |
| 15 | Linear OA(25623, 264, F256, 20) (dual of [264, 241, 21]-code) | [i] | ✔ | |
| 16 | Linear OA(25619, 264, F256, 16) (dual of [264, 245, 17]-code) | [i] | ✔ | |
| 17 | Linear OA(25627, 268, F256, 22) (dual of [268, 241, 23]-code) | [i] | ✔ | |
| 18 | Linear OA(25621, 268, F256, 16) (dual of [268, 247, 17]-code) | [i] | ✔ | |
| 19 | Linear OA(25631, 272, F256, 24) (dual of [272, 241, 25]-code) | [i] | ✔ | |
| 20 | Linear OA(25623, 272, F256, 16) (dual of [272, 249, 17]-code) | [i] | ✔ | |
| 21 | Linear OA(25635, 276, F256, 26) (dual of [276, 241, 27]-code) | [i] | ✔ | |
| 22 | Linear OA(25625, 276, F256, 16) (dual of [276, 251, 17]-code) | [i] | ✔ | |
| 23 | Linear OA(25639, 280, F256, 28) (dual of [280, 241, 29]-code) | [i] | ✔ | |
| 24 | Linear OA(25643, 284, F256, 30) (dual of [284, 241, 31]-code) | [i] | ✔ | |
| 25 | Linear OA(25647, 288, F256, 32) (dual of [288, 241, 33]-code) | [i] | ✔ | |
| 26 | Linear OA(25651, 292, F256, 34) (dual of [292, 241, 35]-code) | [i] | ✔ | |
| 27 | Linear OA(25655, 296, F256, 36) (dual of [296, 241, 37]-code) | [i] | ✔ | |
| 28 | Linear OA(25659, 300, F256, 38) (dual of [300, 241, 39]-code) | [i] | ✔ | |
| 29 | Linear OA(25663, 304, F256, 40) (dual of [304, 241, 41]-code) | [i] | ✔ | |
| 30 | Linear OA(25667, 308, F256, 42) (dual of [308, 241, 43]-code) | [i] | ✔ | |
| 31 | Linear OA(25621, 262, F256, 19) (dual of [262, 241, 20]-code) | [i] | ✔ | |
| 32 | Linear OA(25618, 262, F256, 16) (dual of [262, 244, 17]-code) | [i] | ✔ | |
| 33 | Linear OA(25633, 274, F256, 25) (dual of [274, 241, 26]-code) | [i] | ✔ | |
| 34 | Linear OA(25624, 274, F256, 16) (dual of [274, 250, 17]-code) | [i] | ✔ | |
| 35 | Linear OA(25645, 286, F256, 31) (dual of [286, 241, 32]-code) | [i] | ✔ | |
| 36 | Linear OA(25657, 298, F256, 37) (dual of [298, 241, 38]-code) | [i] | ✔ | |
| 37 | Linear OA(25625, 266, F256, 21) (dual of [266, 241, 22]-code) | [i] | ✔ | |
| 38 | Linear OA(25620, 266, F256, 16) (dual of [266, 246, 17]-code) | [i] | ✔ | |
| 39 | Linear OA(25665, 306, F256, 41) (dual of [306, 241, 42]-code) | [i] | ✔ | |